10 D. Schimmelpfennig et al. Agricultural Economics 23 2000 1–15
the shadow values of capital, livestock and land can be derived as well as the values for public research,
extension, patents and education, which are also cal- culated from the long-run version. The difference be-
tween the rental value and the shadow value indicates whether the factor is over, under or optimally utilized.
Finally, the shadow value of research can be used to derive the rate of ROR investment Huffman, 1987.
Dual measures of technological biases can also be obtained from the profit function. Huffman 1987 sug-
gests a summary measure which provides input and output biases with respect to the conditioning factors
and Khatri 1994 generalizes the conditioning factor biases for a multiple output technology.
4. Data
The national farm-level production data for the pe- riod 1947–1992 were obtained from several sources,
largely RSA 1994, and are described in some de- tail in Thirtle et al. 1993. For both the short- and
long-run profit function specifications, the three out- put aggregates are crops, horticulture, and livestock
and livestock products.
For the short-run profit function, the variable in- puts are Divisia aggregated into four groups: 1 hired
labor; 2 machinery running costs fuel, machinery repairs and other; 3 intermediate inputs fertilizer,
other chemicals, and packing material and 4 live- stock feed and dips. Vehicles and fixed capital in
the form of buildings and other fixed improvements especially irrigation equipment are assumed to be
quasi-fixed in the short run, as are the stocks of ani- mals. The total area of land in the commercial sector
is included as a fixed input.
For the long-run specification, all the conventional inputs are variable. These were Divisia aggregated into
the following groups: 1 hired labor; 2 machinery running costs fuel, machinery repairs and other; 3
intermediate inputs fertilizer, other chemicals, pack- ing material, feed, and dips; 4 capital, particularly
vehicles and other capital in the form of buildings and fixed improvements; 5 livestock and 6 land. The
capital stocks are calculated using US depreciation rates Jorgenson and Yun, 1991, Table 13B, p. 82 in a
PIM that assumes geometric decay, as in Ball 1985. The rental prices of the capital stocks are calculated
using Jorgenson’s formula to derive long-run capital service prices from the assumed depreciation rate and
the real rate of interest.
4
The conditioning factors, that are treated as fixed in- puts in both the short- and long-run specifications, are
public research expenditures, public extension expen- ditures, a rainfall index, world patents
5
and a farmer education index ED. The farmer education index is
the average number of years of secondary education of farmers, which was kindly provided by the South
African Agricultural Union SAAU.
5. Estimation and results
There are too many parameters in the short-run profit function 10 to estimate the full model in
one stage, so the residual profit function approach Bouchet et al., 1989; Khatri et al., 1997 is used. The
system of supply and demand equations, Eqs. 11 and 12, is estimated in the first stage and then the
remaining variables are used to explain the residual. The estimated shadow prices and the input biases
involve both the parameters from the supply and de- mand system, and the residual profit function. How-
ever, as the majority of the parameters for the shadow price and input bias equations are in the supply and
demand system, the parameters used in the residual profit function most of which are significant can
be treated as constants. This allows the derivation of indicative significance bounds for the shadow price
and input bias estimates.
6
The system of output supply and variable input de- mand equations are estimated for both the short-run
and the long-run using the iterative Zellner or seem- ingly unrelated procedure. Each system, with symme-
try imposed, produces a set of parameter estimates not reported here, most of which are significant at
the 5 confidence level. The coefficients of determi- nation R
2
’s of the estimated individual supply and demand equations for both the short-run and long-run
4
We thank Eldon Ball for constructing these series.
5
The patent data comes from the US patent database compiled at the University of Reading by John Cantwell. The series are
patent counts, for all agriculture-related chemical and mechanical patents registered in the US.
6
The US TFP index was not included in the profit function esti- mation, both to preserve degrees of freedom and because variable
deletion tests applied to the two-stage approach indicated that it had no explanatory power.
D. Schimmelpfennig et al. Agricultural Economics 23 2000 1–15 11
specifications vary between 0.87 and 0.99, which is high even for time series models. The Durbin–Watson
statistics indicate that there are no problems of se- rial correlation in the individual equations. Further,
although homogeneity remains a maintained assump- tion implicitly imposed when normalizing, symme-
try and monotonicity, which are necessary conditions for global convexity, are both satisfied by the estimated
systems. The estimated profit functions are thus found to be acceptable both with respect to their statistical
performance and theoretical consistency.
The results obtained with the short-run and long-run profit functions that can be estimated in one stage,
specifically the elasticity estimates, are in accordance with expectations. The elasticities of the outputs and
variable inputs in the long- and short-run estimations are remarkably similar. They are not repeated here
as they are almost identical to the short-run profit function results reported by Khatri et al. 1995.
As expected, the long-run elasticities for land, cap- ital and livestock are consistently higher than the
short-run elasticities. It can therefore be concluded that the results from the short- and long-run models
are consistent.
The elasticities show the low supply response of South African agriculture, even over the long run. This
result corresponds very closely with the findings of van Zyl 1986 and Sartorius von Bach and van Zyl 1991.
It also confirms earlier comments on the abnormal development path of South African agriculture World
Bank, 1994; Kirsten and van Zyl, 1996.
The estimates of the factor-saving biases of techni- cal change show that the Hicks neutrality assumption
implicit in the two-stage model is rejected, which is contrary to assumptions implicit in the two-stage ap-
proach and may have biased the results. Public RD has been capital and intermediate input using, and
labor and animal input saving. This pattern is typical of developed countries and is hardly appropriate for
a country with abundant cheap labor and high rural unemployment. Thus, the public RD system has
exacerbated the damage done by apartheid policies discussed above.
5.1. Shadow prices Khatri et al. 1998a established that the shadow
price of land is positive, but for livestock, it was not
Table 1 Estimated shadow values of the conditioning variables evaluated
at the variable means
a
Factor Short-run
specification Long-run
specification Public research
4.04 323.5
International patents 0.23
342.8 Public extension
−0.012 −290.6
Farmer education −1378.5
−6867.2
a
Note: All the shadow prices are significant at the 0.05 level; shadow values of the short- and long-run conditioning variables
are not directly comparable due to differences in the units of measurement of the capital items.
significantly different from zero and for capital it was negative, indicating that policies to reduce capital use
could have increased profit. More importantly, they found that the capital stock took 11 years to adjust to
changes in input prices. This paper concentrates on the shadow values of the technology variables, which can
be interpreted as the marginal change in profits from a unit increment in a technology-related variable. The
shadow value for RD can be used to derive the rate of ROR investment see Khatri et al., 1996. Note, how-
ever, that the shadow values of the short- and long-run conditioning variables are not directly comparable due
to differences in the units of measurement of the cap- ital items. These shadow values are reported in Table
1 for both the short- and long-run specifications, eval- uated at the variable means.
In both the short and the long run, public RD expenditures and international patents have positive
and highly significant shadow values, indicating that both the national research system and private sector
spill-ins benefit South African agriculture. The two are related in that much of the public research is adaptive
in nature and is geared towards exploiting technology that has been developed abroad. The shadow price for
public research was negative at the beginning of the period, after which the value rose at an increasing
rate, suggesting that the public research system is now making a considerable contribution to profitability see
van Zyl et al., 1993.
The shadow price of extension is surprisingly small although highly significant in the short-run formu-
lation, implying a very low return on public exten- sion expenditure of only 3, while in the long run,
it is negative. This indicates that extension expendi-
12 D. Schimmelpfennig et al. Agricultural Economics 23 2000 1–15
tures were too high. Similarly, the education index ap- pears to have considerable explanatory power in both
the short- and long-run formulations, but the shadow price is negative. Since education is a proxy for man-
agerial ability, this is contrary to expectations, but this negative result and the weak contribution of extension
expenditures are probably related.
The shadow value of education was positive until the early 1960s, but has become increasingly nega-
tive since then, and the shadow price of extension has been falling over the period, which suggests that South
African commercial farmers have become less depen- dent on public extension advice. This corresponds with
the findings of Koch et al. 1991, who show that gov- ernment extension officers spend increasingly more
time on administrative duties and do very little ac- tual extension work. Thus, the decline in extension
effort could explain the low payoff, but so could re- duced need for extension. The education level of South
African commercial farmers is relatively high, so it is entirely possible that the minimum level required
to assimilate mass produced research and extension messages has been reached.
But there is a more radical explanation that is far more specific to South Africa. The unreported fixed
factor elasticities show that all the input and output elasticities with respect to education are positive, and
all but one are highly significant. Thus, education aug- ments output but it also augments input use, more than
proportionately in the case of non-labor inputs. As crop production expanded into climatically marginal
and more risky areas, intermediate input use and mech- anization increased considerably in the period from
1965 to the early 1980s van Zyl et al., 1995. There was evidence of over-mechanization van Zyl et al.,
1987 and fertilizer was often applied on extension service advice up to levels where it actually decreased
output Korentajer et al., 1989. This was especially disastrous in the bad climatic conditions of the early
and late 1980s van Rensburg and Groenewald, 1987. Sartorius von Bach et al. 1992 clearly show that it
was the better educated farmers who adopted these practices to a greater extent. Thus, educated farmers
did respond more strongly to extension service ad- vice, but because maximum physical production as
opposed to maximizing profit was the major goal and focus of the agricultural research and extension
system, the effects were negative. 5.2. Internal rate of return
The shadow prices reported above are hard to inter- pret because the technology variables have no obvious
prices, and thus, there is no way to compare whether there has been over or under investment. Therefore,
the effectiveness of public RD expenditures can be better interpreted by calculating rates of return ROR.
The shadow values represent the imputed marginal value of a unit increase in knowledge stocks. Thus, to
estimate the marginal internal rate of return MIRR to research, the additional flow of research investment
required to change current knowledge stocks by one unit must be calculated and this will depend on the
length and shape of the lag. The MIRR will vary with the choice of the number of periods over which the in-
cremental research is distributed. Research is found to affect productivity for 9 years, so the MIRRs reported
in Table 2 are for this period of incremental research investments resulting in a unit change in the knowl-
edge stock. The rate of interest that equates this in- cremental research expenditure to the shadow price is
the MIRR Ito, 1991.
The net output value minus input costs ROR for the short-run profit function is 44, while the long-run
result is 113. The lower value is perhaps reasonable for a research system that is to some extent free-riding
on the investments made by others. The long-run re- sult is not as high as for the two-stage model, but it is
2.6 times the short-run result. The return will be higher because of the effects of new technology embodied in
new capital equipment. Thus, the difference between the two results should depend on the fact that the cap-
ital stocks are allowed to adjust in the long-run case. This raises a new problem, since Khatri et al. 1995
found that the capital stock adjusted to changes in the real rate of interest with a long lag of 11 years. The
Table 2 Estimated returns to RD
Lag length Short-run
specification Long-run
specification 5 years
44 113
a
11 years –
58
b a
Lag length appropriate for variable long-run inputs see dis- cussion in Section 5.2.
b
Lag length appropriate for an average of fixed and quasi-fixed long-run factors.
D. Schimmelpfennig et al. Agricultural Economics 23 2000 1–15 13
12–13-year lag for the patent series, reported above, corroborates this period of adjustment. This suggests
that, although the negatively skewed 9-year lag, with a peak effect after 2 years, may be appropriate for
the short-run profit function, it is hard to reconcile with long-run adjustments in fixed or quasi-fixed fac-
tors. Therefore, the short lag may be appropriate for RD on variable inputs like seed varieties and agro-
nomic improvements, but RD on capital items like irrigation equipment, cultivation implements and other
specialized machinery must take longer than 2 years to have a peak effect. The difference between the
short-run and long-run RORs should result from the technology that is embodied in the capital items. If
this is so, then the effects will only occur when the capital stock has adjusted.
To take the adjustment period of 11 years into ac- count, without knowing the lag distribution, the MIRR
for the long run is calculated with a lag of 11 years be- tween the unit increment in the knowledge stock and
the shadow value. This gives the last figure in Table 2, of 58, which may be a more realistic estimate of
the long-run net ROR. These are certainly respectable rates of return on public expenditure, with the usual
qualifications that the figures may be somewhat dimin- ished if we adjust for the dead-weight losses associ-
ated with tax collection and the possibility that public funding may be crowding out private sector research.
Of greater interest is the sensitivity of ROR calcula- tions to assumed lag structure, particularly when the
lag in the effect of RD on TFP is skewed, negatively in this case, so benefits are exposed to less discounting
than if the lag structure were to be symmetric.
6. Conclusion
